广义系统的H2次优控制问题的一个LMIs条件

研究具有动态输出反馈的连续广义系统的H2次优控制问题.在H2范数的时域计算 方法的基础上,关于连续广义系统进行了H2次优性能分析,得到了满足H2次优性能的线性矩 阵不等式组的充要条件.其次,利用线性矩阵不等式(LMI)方法设计了H2次优动态输出反馈 控制器.最后,通过数值例子进一步说明了该文的设计方法.     

非线性系统零解稳定性判定的广义二次型方法

为了寻找一种能充分利用矩阵理论构造非线性系统李亚普诺夫函数的方法．首先提出分量函数矩阵和广义二次型函数等概念，得到了如果一个函数的导数具有某种特定形式。则不需处理旋度方程．便可直接得到该函数的若干定理；然后提出一种构造李亚普诺夫函数和判定非线性系统零解稳定性的广义二次型方法．并举例说明了该方法的应用．理论和实例表明，该方法是一种充分利用矩阵特性，适用范围广且不需处理旋度方程的方法．     

随机线性系统模型的集结简化

讨论集结法在简化随机线性系统模型中的应用，它可将n维状态空间模型的主要特征集结简化到r维（r〈n）状态空间模型上，优化地再现原系统的基本性能和模裂数据。在简化模型中，动态系统集结矩阵选定为原系统矩阵特征值的子集。这种方法既适用于离散系统，也适用于连续系统。高阶系统动态模型的这种简化处理方法，不仅克服与避免了对这类系统进行仿真分析时，占用较大内存空间与耗费大量机时的缺陷，而且提高厂仿真与控制过程的稳定性和结果的准确性。     

逆系统方法中非线性系统状态观测器的应用

将Lipschitz非线性系统状态观测器设计方法应用于非线性系统的逆系统方法设计中,解决了在利用逆系统方法实现非线性系统反馈线性化的过程中由于系统状态的不可知,而使系统不能满足反馈补偿的问题。针对以往的Lipschitz非线性系统状态观测器设计方法中通过Riccati方程对增益矩阵的求取过程比较繁琐的问题,着重讨论了采用线性矩阵不等式来改进增益矩阵的求取方法,利用Matlab中的LMI工具箱对其进行求取,计算简单,并给出了证明。最后通过实例仿真,验证了方法的有效性。     

基于矩阵测度的非线性广义时滞系统鲁棒模糊控制

研究T-S模糊广义时滞系统的鲁棒控制问题.不同于传统的寻求公共正定矩阵的方法,基于矩阵测度给出保证系统鲁棒稳定的充分条件,并将此条件进一步转化为线性矩阵不等式.通过求解线性矩阵不等式,得到状态反馈控制器和静态输出反馈控制器.最后通过算例仿真验证了方法的有效性.     

Analysis of robust stability for switched systems with multiple time-delays

The sufficient conditions of delay-dependent exponential stability for switched systems and robust exponential stability for uncertain switched systems with two time-delays are presented by using average dwell time method and free-weighting matrix method.The interaction between different time-delays is considered.The sufficient conditions do not need that every subsystem is stable.The designed methods of the switching law are also given.The sufficient conditions are given in the form of linear matrix inequalities that can be solved easily.The result is proven to be valid by the simulation at last.     

Stable solution of instable systems of linear equations with a band matrix

Teh evaluation of large linear systems with a band matrix was done in [1] by reducing the given system to some little ones. However, there were investigated in detail only stable systems. Here we modify the method of [1] in such a way that it yields a solutionalso for instable systems, the most components of which are stable. We attain this effect by constructing a suitable outer inverse instead of the usual inverse matrix. To illustrate the method we solve approximately systems of linear equations with a tri-diagonal matrix.     

状态饱和离散线性系统的稳定性分析

讨论一类具有状态饱和非线性的离散线性系统稳定性分析问题. 通过引入无穷范数小于等于1 的自由矩阵与对角元素非正的对角矩阵, 将状态饱和离散线性系统的状态变量约束在一个凸多面体内, 进而以矩阵不等式形式给出状态饱和离散线性系统的稳定性判据, 并给出该矩阵不等式的迭代线性矩阵不等式算法. 基于这一稳定性判据, 给出了基于迭代线性矩阵不等式的状态反馈控制律设计算法. 通过状态饱和离散线性系统的状态空间分割方法, 给 出了保守性更小的稳定性判据, 并给出了相应的迭代线性矩阵不等式算法. 数值例子验证了所给出方法的正确性与有效性.

     

Max–plus matrix method and cycle time assignability and feedback stabilizability for min–max–plus systems

A variety of problems arising in nonlinear systems with timing constraints such as manufacturing plants, digital circuits, scheduling managements, etc., can be modeled as min–max–plus systems described by the expressions in which the operations minimum, maximum and addition appear. This paper applies the max–plus matrix method to analyze the cycle time assignability and feedback stabilizability of min–max–plus systems with min–max–plus inputs and max–plus outputs, which are nonlinear extensions of the systems studied in recent years. The max–plus projection matrix representation of closed-loop systems is introduced to establish some structural and quantitative relationships between reachability, observability, cycle time assignability and feedback stabilizability. The necessary and sufficient conditions for the cycle time assignability with respect to a state feedback and an output feedback, respectively, and the sufficient condition for the feedback stabilizability with respect to an output feedback are derived. Furthermore, one output feedback stabilization policy is designed so that the closed-loop systems take the maximal Lyapunov exponent as an eigenvalue. The max–plus matrix method based on max–plus algebra and directed graph is constructive and intuitive, and several numerical examples are given to illustrate this method.     

离散-连续混合系统输出公式——Mason公式的推广应用

本文用矩阵方程建立了离散-连续混合系统的数字模型,并由此推导出混合系统的输出公 式,该公式是Mason公式在混合系统中的推广.本文讨论了混合系统的另外两种解法,即矩 阵法和构图法. 本文结论与文献[3]有所不同.     

Calculating fuzzy inverse matrix using fuzzy linear equation system

Linear equation systems play a very important role in engineering, mathematics, statistics and other disciplines. Fuzzifying either parameters or variables or both in these systems has been one of the research areas in the fuzzy literature since these kinds of systems are encountered in many applications. These systems are generally called fuzzy linear equations. Various types of these models have been examined for a decade. The solution procedures of these systems depend on different methods such as extension principle and interval arithmetic. Also, the method which is often used in computing inverse of a matrix in real case could be extended to fuzzy case, which employs linear equation system and identity matrix. For this purpose, we propose a new method which includes some new definitions which are fuzzy zero number, fuzzy one number and fuzzy identity matrix. Based on these definitions, direct computation of fuzzy inverse matrix is done using fuzzy arithmetic and fuzzy equation system. Actually, this simply extends the notion used in real case to fuzzy case. Calculation is realized with two different settings. While the first one is called direct numerical solution, the other is obtained by choice of decision maker. It is noted that the uniqueness of the calculated fuzzy inverse matrix is not guaranteed.     

Linear systems with non-stationary random inputs†

This paper concerns the response correlation matrix of a linear time variable system with stationary or non-stationary stochastic inputs modulated by linear homogeneous operators. By adapting Lanczos' ‘selected points’ method an algorithm is introduced to compute the state covariance matrix of systems with deterministic initial state. Certain computational features of response correlation matrices of systems with random initial state and random inputs are also outlined. Limited numerical studies indicate that the proposed method is efficient to treat uni-dimensional and small-order multi-dimensional systems. Mean square response comparisons with some of the previously studied systems indicate good agreement and the saving in machine time appears to be substantial.     

转移概率部分未知时滞跳变系统有限时间控制

时滞是许多工业系统的固有特性,会导致系统控制性能的下降,甚至影响系统稳定,而在实际系统中,有限时间系统的特性更值得关注。针对上述情况,对一类具有时滞的马尔可夫跳变系统有限时间控制器设计的问题进行了研究。把转移概率完全已知的条件放宽至部分未知的更一般情形,采用自由权重的方法,保证所得的线性矩阵不等式具有更小的保守性。首先,给出马尔科夫跳变系统有限时间有界性、有限时间 H无穷有界性的判定准则。然后,通过对线性矩阵不等式(LMIs)求解,获得状态观测器和状态反馈控制器的增益矩阵。最后,仿真实例验证所提算法的有效性。     

动态区间系统的最优保性能控制--LMI方法

针对动态区间系统和一个给定的二次型性能指标,研究了其保性能控制问题,基于线性矩阵不等式(LMI)提出了最优保性能控制器设计方法,并将相关结果推广到参数不确定系统.利用功能强大的LMI工具,求解非常方便.所给实例表明,该方法用于设计动态区间系统与秩-1型参数不确定系统的最优保性能控制器,非常有效.     

Guaranteed cost control of uncertain discrete‐time singular Markov jump systems with indefinite quadratic cost

The guaranteed cost control problem for discrete‐time singular Markov jump systems with parameter uncertainties is discussed. The weighting matrix in quadratic cost function is indefinite. For full and partial knowledge of transition probabilities cases, state feedback controllers are designed based on linear matrix inequalities method which guarantee that the closed‐loop discrete‐time singular Markov jump systems are regular, causal and robust stochastically stable, and the cost value has a zero lower bound and a finite upper bound. A numerical example to illustrate the effectiveness of the method is given in the paper. Copyright © 2010 John Wiley & Sons, Ltd.     

A new decentralised controller design method for a class of strongly interconnected systems

In this paper, two interconnected structures are first discussed, under which some closed-loop subsystems must be unstable to make the whole interconnected system stable, which can be viewed as a kind of strongly interconnected systems. Then, comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown. A new approach for the design of decentralised controllers is presented by determining the Lyapunov function structure previously, which allows the existence of unstable subsystems. By fully utilising the orthogonal space information of input matrix, some new understandings are presented for the construction of Lyapunov matrix. This new method can deal with decentralised state feedback, static output feedback and dynamic output feedback controllers in a unified framework. Furthermore, in order to reduce the design conservativeness and deal with robustness, a new robust decentralised controller design method is given by combining with the parameter-dependent Lyapunov function method. Some basic rules are provided for the choice of initial variables in Lyapunov matrix or new introduced slack matrices. As byproducts, some linear matrix inequality based sufficient conditions are established for centralised static output feedback stabilisation. Effects of unstable subsystems in nonlinear Lur'e systems are further discussed. The corresponding decentralised controller design method is presented for absolute stability. The examples illustrate that the new method is significantly effective.     

状态反馈极点配置问题

本文研究了线性时不变多变量系统引进状态反馈任意配置闭路极点问题,首先导出了系统的一种新的标准型,然后给出了计算状态反馈矩阵的一种新方法,其主要的运算是解一组含有n-p+1个未知数的线性代数方程,算法简单,然后举例说明了这种方法的应用。文中同时还证明了状态反馈闭路系统特征方程可以分解为二个多项式之积,其阶数分别为n-p+1和p-1,而其系数为反馈矩阵元素的线性函数。     

An Implicit Transition Matrix Approach to Stability Analysis of Flexible Multi-Body Systems

The stability of linear systems defined by ordinarydifferential equations with constant or periodic coefficients can beassessed from the spectral radius of their transition matrix. Inclassical applications of this theory, the transition matrix isexplicitly computed first, then its eigenvalues are evaluated; if thelargest eigenvalue is larger than unity, the system is unstable. Theproposed implicit transition matrix approach extracts the dominanteigenvalues of the transition matrix using the Arnoldi algorithm,without the explicit computation of this matrix. As a result, theproposed implicit method yields stability information at a far lowercomputational cost than that of the classical approach, and is ideallysuited for stability computations of systems involving a large number ofdegrees of freedom. Examples of application of the proposed methodologyto flexible multi-body systems are presented that demonstrate itsaccuracy and computational efficiency.     

融合矩阵分解与距离度量学习的社会化推荐算法

为解决传统推荐系统中存在的冷启动难题,基于距离反映偏好的假设提出了一种融合矩阵分解与距离度量学习的社会化推荐算法。该算法同时对样本和距离度量进行训练,在满足距离约束的前提下更新距离度量和用户与项目的坐标,并将用户与项目嵌入到统一的低维空间,利用用户与项目之间的距离生成推荐结果。基于豆瓣和Epi-nions数据集的对比实验结果验证了该方法可有效提高推荐系统的可解释性和精确度,明显优于基于矩阵分解的推荐方法。研究结果表明,所提方法缓解了传统推荐系统中存在的冷启动问题,为推荐系统的研究提供了另一种可供参考的研究思路。     

不确定离散广义系统的D稳定鲁棒控制

研究了具有圆盘区域极点约束的一类不确定离散广义系统的鲁棒控制问题.首先,研 究了控制输入项不含扰动的不确定离散广义系统,提出了广义二次D镇定的概念,基于矩阵不 等式和广义Riccati方程,给出了一种广义二次D镇定器的设计方法,所得到的结论能够实现研 究目标;然后,讨论了控制输入项含有扰动的不确定离散广义系统,在一定的假设条件下,给出 了期望状态反馈增益阵的存在条件及其解析表达式.最后,用数值示例说明所给方法的有效性 及可行性.